If you have suitable access to SSIS, you might be able to try this:

1) Set up the subscription on the report server fro a date already passed

2) Identify the ID of the SQL Job that represents that subscription

3) Run the subscription SQL job from an SSIS "Run SQL Job" task

4) You should be able to write a script in the SSIS that identifies both whether the last run of the job was successful AND whether it is the right day. The precendence can be set to run the SQL job if the script task is successful.

This is one of the ways we synchronise a data import with the delivery of a report by a subscription so that the report does not get delivered before a its data has been successfully imported.